Problem: Solve for $x$ : $ 2|x + 2| - 7 = 5|x + 2| + 6 $
Solution: Subtract $ {2|x + 2|} $ from both sides: $ \begin{eqnarray} 2|x + 2| - 7 &=& 5|x + 2| + 6 \\ \\ {- 2|x + 2|} && {- 2|x + 2|} \\ \\ -7 &=& 3|x + 2| + 6 \end{eqnarray} $ Subtract $6$ from both sides: $ \begin{eqnarray} -7 &=& 3|x + 2| + 6 \\ \\ {- 6} && {- 6} \\ \\ -13 &=& 3|x + 2| \end{eqnarray} $ Divide both sides by ${3}$ $ \dfrac{-13} {{3}} = \dfrac{3|x + 2|} {{3}} $ Simplify: $ -\dfrac{13}{3} = |x + 2| $ The absolute value cannot be negative. Therefore, there is no solution.